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Functions and commands 345
Lagrange Given a vector of abscissas and a vector of ordinates, returns
the Lagrange polynomial for the points specified in the two
vectors. This function can also take a matrix as argument, with
the first row containing the abscissas and the second row
containing the ordinates.
lagrange([X1 X2…], [Y1 Y2…]))
or
lagrange
Example:
lagrange([1,3],[0,1]) gives (x-1)/2
Laguerre Given an integer n, returns the Laguerre polynomial of degree n.
laguerre(Integer))
Example:
laguerre(4) returns 1/24*a^4+(-1/6)*a^3*x+5/
12*a^3+1/4*a^2*x^2+(-3/2)*a^2*x+35/24*a^2+(-
1/6)*a*x^3+7/4*a*x^2+(-13/3)*a*x+25/12*a+1/
24*x^4+(-2/3)*x^3+3*x^2-4*x+1
Legendre Given an integer n, returns the Legendre polynomial of degree
n.
legendre(Integer)
Example:
legendre(4) returns
Chebyshev Tn Given an integer n, returns the Tchebyshev polynomial (of the
first kind) of degree n.
tchebyshev1(Integer)
Example:
tchebyshev1(3) gives 4*x^3-3*x
Chebyshev Un Given an integer n, returns the Tchebyshev polynomial (of the
second kind) of degree n.
tchebyshev2(Integer)
Example:
tchebyshev2(3) gives 8*x^3-4*x
X1 X2 ...
Y1 Y2 ...
35
8
-------
x
4
15
4
-------
x
2
3
8
---
++